Inductive Pairwise Ranking: Going Beyond the n log(n) Barrier

We study the problem of ranking a set of items from nonactively chosen pairwise preferences where each item has feature information with it. We propose and characterize a very broad class of preference matrices giving rise to the Feature Low Rank (FLR) model, which subsumes several models ranging from the classic Bradley-Terry-Luce (BTL) (Bradley and Terry 1952) and Thurstone (Thurstone 1927) models to the recently proposed blade-chest (Chen and Joachims 2016) and generic low-rank preference (Rajkumar and Agarwal 2016) models. We use the technique of matrix completion in the presence of side information to develop the Inductive Pairwise Ranking (IPR) algorithm that provably learns a good ranking under the FLR model, in a sample-efficient manner. In practice, through systematic synthetic simulations, we confirm our theoretical findings regarding improvements in the sample complexity due to the use of feature information. Moreover, on popular real-world preference learning datasets, with as less as 10% sampling of the pairwise comparisons, our method recovers a good ranking.

[1]  John B. Shoven,et al.  I , Edinburgh Medical and Surgical Journal.

[2]  R. A. Bradley,et al.  RANK ANALYSIS OF INCOMPLETE BLOCK DESIGNS THE METHOD OF PAIRED COMPARISONS , 1952 .

[3]  J. Marschak.  Binary Choice Constraints on Random Utility Indicators , 1959 .

[4]  R. Luce,et al.  Individual Choice Behavior: A Theoretical Analysis. , 1960 .

[5]  R. Duncan Luce,et al.  Individual Choice Behavior: A Theoretical Analysis , 1979 .

[6]  L. Thurstone.  A law of comparative judgment. , 1994 .

[7]  Thorsten Joachims,et al.  Optimizing search engines using clickthrough data , 2002, KDD.

[8]  Shotaro Akaho,et al.  Efficient Clustering for Orders , 2006, Sixth IEEE International Conference on Data Mining - Workshops (ICDMW'06).

[9]  Atri Rudra,et al.  Ordering by weighted number of wins gives a good ranking for weighted tournaments , 2006, SODA '06.

[10]  Jieping Ye,et al.  An accelerated gradient method for trace norm minimization , 2009, ICML '09.

[11]  Emmanuel J. Candès,et al.  Exact Matrix Completion via Convex Optimization , 2009, Found. Comput. Math..

[12]  Craig Boutilier,et al.  Learning Mallows Models with Pairwise Preferences , 2011, ICML.

[13]  Yi Ma,et al.  Robust principal component analysis? , 2009, JACM.

[14]  Emmanuel J. Candès,et al.  Exact Matrix Completion via Convex Optimization , 2008, Found. Comput. Math..

[15]  Manuela Cattelan,et al.  Models for Paired Comparison Data: A Review with Emphasis on Dependent Data , 2012, 1210.1016.

[16]  Scott Sanner,et al.  Learning Community-Based Preferences via Dirichlet Process Mixtures of Gaussian Processes , 2013, IJCAI.

[17]  Inderjit S. Dhillon,et al.  Provable Inductive Matrix Completion , 2013, ArXiv.

[18]  Ariel D. Procaccia,et al.  When do noisy votes reveal the truth? , 2013, EC '13.

[19]  Miao Xu,et al.  Speedup Matrix Completion with Side Information: Application to Multi-Label Learning , 2013, NIPS.

[20]  Venkatesh Saligrama,et al.  A Topic Modeling Approach to Rank Aggregation , 2014 .

[21]  Venkatesh Saligrama,et al.  A Topic Modeling Approach to Ranking , 2015, AISTATS.

[22]  Inderjit S. Dhillon,et al.  Matrix Completion with Noisy Side Information , 2015, NIPS.

[23]  Thorsten Joachims,et al.  Modeling Intransitivity in Matchup and Comparison Data , 2016, WSDM.

[24]  Arun Rajkumar,et al.  When can we rank well from comparisons of \(O(n\log(n))\) non-actively chosen pairs? , 2016, COLT.